1. Field of the Invention
The present invention relates to a frequency demodulator and, more specifically, to a digital frequency demodulator for performing digital demodulation using a phase shift mode of operation. A corresponding method is also disclosed.
The present application is based on Korean Patent Application No. 93-18014, which is incorporated herein by reference for all purposes.
2. Brief Discussion of Related Art
In general, a frequency demodulator is used to restore a signal, which was frequency-modulated for transmission, back into the original signal, i.e., before transmission. Frequency demodulation has been conventionally carried out in an analog mode of operation. However, due to the inherent characteristics of the analog circuit components, the signal-to-noise (S/N) ratio of a demodulated signal is generally lower, as is the linearity, sensitivity and stability of the system.
In order to overcome such problems with analog frequency demodulation, a conventional digital frequency demodulator has been proposed, as shown in FIG. 1. Prior to the description of the conventional digital frequency demodulator of FIG. 1, a brief discussion of analog frequency modulation will be provided.
Basically, frequency modulation varies a carrier frequency in accordance with a modulation signal. In an exemplary case, fixed data corresponding to the carrier frequency is added to data in which a frequency deviation constant is multiplied by a video signal, so as to obtain data corresponding to an instant frequency. If this data is integrated, the data indicates an instant phase. That is, when the data is normalized for a period of 2.pi., a predetermined angle change occurs to its phase during one clock period and then a signal corresponding to the magnitude of the angle is output. This signal is the frequency-modulated signal.
This process can be expressed using equation (1): ##EQU1## where A is the amplitude of an information signal (the modulating signal); .omega..sub.C is the carrier frequency; D.omega. is frequency deviation angular velocity; .theta. is the initial phase; and x(t) is the information signal.
If equation (1) is changed into an equation which is sampled over a period T, equation (2) follows thus: ##EQU2## where .theta. is zero; K2 is equal to f.sub.C T, which determines the carrier frequency; and K1 is equal to D.sub.f T, which is a factor for determining the frequency deviation.
Frequency demodulation for restoring the FM signal to its original form is carried out as follows.
First, by substituting .PHI. for the bracketed expression of equation (2), we get EQU Y.sub.FM (nT)=Asin.PHI. (3)
and solving for .PHI. in equation (3), ##EQU3## which may be expressed in terms of X and Y as ##EQU4##
Therefore, in order to restore the frequency modulated signal into the original signal as shown in equations (4), (5) and (6), the conventional frequency demodulator of FIG. 1 will be explained below.
An input signal in the form of a sine wave is applied to, a phase shifter 12, which delays the input signal for -.pi./2 so as to output a cosine wave. Simultaneously, a first delay 11 delays the applied sine wave for a predetermined time, e.g., the processing time in phase shifter 12, so that the cosine wave, i.e., the input signal, phase-shifted by 90.degree., from the phase shifter 12 is output at the same time as the sine wave from the first delay 11. A magnitude discriminator 13 compares the magnitude of the absolute value of the sine wave output from first delay 11 and the magnitude of the absolute value of the cosine wave output from phase shifter 12. Based on this comparison, if the absolute value of the cosine wave is greater than or equal to that of the sine wave, a divider 14 produces a tangent form of the input signal, as an address signal. When the absolute value is less than that of the sine wave, the cotangent form is output as the address signal. Look-up table 40 reads out and outputs a signal corresponding to the address signal output from divider 14.
Meanwhile, a quadrant discriminator 20 detects the signs of the applied sine and cosine waves in order to discriminate the quadrant of the signal being demodulated. Then, a second delay 30 delays the quadrant discriminating signal output from quadrant discriminator 20 for a time equal to the time during which data is read out from look-up table 40.
An operating device 50 operates on the signal output from look-up table 40 according to the quadrant discriminating signal output from second delay 30. A differentiator 60 then differentiates the signal output from operating device 50 so as to restore the signal integrated during the frequency modulation. A subtractor 70 subtracts a carrier frequency K2 from the signal output from differentiator 50 so as to cancel the carrier frequency from the signal output from differentiator 50 and output a signal without the K2 component. Then, a multiplier 80 multiplies the applied signal by 1/K1, thereby canceling the frequency deviation determining component K1. Finally, a low-pass filter 90 removes the high frequency component of the restored signal and outputs the frequency demodulated signal.
In the conventional digital frequency demodulator shown in FIG. 1, since a signal, which is generated when the high frequency component of a frequency-modulated signal is not faithfully reproduced by a head, is applied as the input and demodulated, a black-and-white inversion phenomenon occurs on the screen, as illustrated in FIG. 2. In FIG. 2, the original signal S.sub.1 is overlaid on the reproduced signal S.sub.2. It will be noted that black-and-white inversion occurs in the central region of FIG. 2.